3 Proportional & Linear Functions

Edit 0 8 …
Unit 3 Proportional & Linear Functions
Students will understand:
  • A proportional relationship is a set of equivalent rates
  • In a rate of change, the dependent variable is written in the numerator and the independent variable is written in the denominator.
  • Interpret unit rate as the slope of a proportional relation
  • Proportional relationships have a y-intercept of 0
Students will be able to:
  • Given a context, write and use linear equations of proportional relationships of the form y = mx
  • Given a context, write and use linear equations of the form y = mx + b
  • Create & use multiple representations of linear functions
  • Compare two linear functions graphed on the same axes
  • Compare multiple representations and discuss their advantages/disadvantages
  • Compare properties of two functions, each presented in a different way
  • Choose an appropriate scale on a graph
  • Use similar triangles to explain why the slope (unit rate) m is the same between any two distinct points on a non-vertical line in the coordinate plane
  • Differentiate between proportional and non-proportional relationships
  • Give examples of functions that are not linear (e.g. absolute value, area of a square, and volume of a cube)
Warmups & Exits Days 2-6
http://dl.dropbox.com/u/34080806/Proportional%20Warmups/Linear%20Warmups.docx

Day
 Learning Activities
 Objective
1
 “Filling the Gas Tank”
 Understand proportional relationships.
2-3
 Walking Rates 1
 Understand the proportional relationship, .
4-5
 Walking Rates 2
 Connecting similar triangles and slope.
6
Compare two different proportional relationships represented in different ways.
7
 “Wash the Car and Fill the Gas Tank”
 Compare proportional and linear.
8
 “The Swimathon”
 Compare different linear functions.
9
 Carnegie 2-4: “Linear Functions”
Linear functions in context.
10
 Carnegie 2-5: “Using Tables, Graphs and Equations Part 1”
 Compare different representations.
11
 Carnegie 2-6: “Using Tables, Graphs and Equations Part 2”
 Analyze two linear functions graphed on same coordinate graph.
12
 Carnegie 2-7: “Introduction to Non-Linear Functions”
 Graph absolute value function, Area and volume as functions of side length.
13
 Test Review
14
 TEST: Linear Functions


home